Practical Geometry (Constructions) - EXERCISE 18.1 | Mathematics (Maths) Class 8 PDF Download

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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.1                                                  PAGE NO: 18.4 
 
1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 
cm, DA = 3.8 cm and BD = 6.6 cm. 
Solution: 
The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 
cm. 
Divide the quadrilateral into two triangles i.e., ?ABD and ?BCD 
Steps to construct a quadrilateral: 
Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm. 
Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as 
centre and radius CD = 6.4 cm. 
Step 3- Now join the intersection point from B and D and label it as C. 
Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. 
Do the same by taking D as center and radius DA = 3.8cm. 
Step 5- Join the intersection point from B and D and label it as A. 
 
 
2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 
6.3 cm, AC = 9.4 cm Measure BD. 
Solution: 
The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm 
Measure BD. 
Steps to construct a quadrilateral: 
Step 1- Draw a line segment AB = 5.5cm 
Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C. 
Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C. 
Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D. 
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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.1                                                  PAGE NO: 18.4 
 
1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 
cm, DA = 3.8 cm and BD = 6.6 cm. 
Solution: 
The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 
cm. 
Divide the quadrilateral into two triangles i.e., ?ABD and ?BCD 
Steps to construct a quadrilateral: 
Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm. 
Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as 
centre and radius CD = 6.4 cm. 
Step 3- Now join the intersection point from B and D and label it as C. 
Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. 
Do the same by taking D as center and radius DA = 3.8cm. 
Step 5- Join the intersection point from B and D and label it as A. 
 
 
2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 
6.3 cm, AC = 9.4 cm Measure BD. 
Solution: 
The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm 
Measure BD. 
Steps to construct a quadrilateral: 
Step 1- Draw a line segment AB = 5.5cm 
Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C. 
Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C. 
Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D. 
Step 6- Now join BC, CD and AD 
Measure of BD is 5.1cm. 
 
 
3. Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 
cm, WX = 3 cm and XZ = 9 cm. 
Solution: 
The given details are XY = 5cm, YZ = 6cm, ZW = 7cm, WX = 3cm and XZ = 9cm. 
Steps to construct a quadrilateral: 
Step 1- Draw line XZ of length 9cm. 
Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z 
as centre and radius ZY = 6cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. 
Similarly, taking Z as the center and radius ZW = 7cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
 
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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.1                                                  PAGE NO: 18.4 
 
1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 
cm, DA = 3.8 cm and BD = 6.6 cm. 
Solution: 
The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 
cm. 
Divide the quadrilateral into two triangles i.e., ?ABD and ?BCD 
Steps to construct a quadrilateral: 
Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm. 
Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as 
centre and radius CD = 6.4 cm. 
Step 3- Now join the intersection point from B and D and label it as C. 
Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. 
Do the same by taking D as center and radius DA = 3.8cm. 
Step 5- Join the intersection point from B and D and label it as A. 
 
 
2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 
6.3 cm, AC = 9.4 cm Measure BD. 
Solution: 
The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm 
Measure BD. 
Steps to construct a quadrilateral: 
Step 1- Draw a line segment AB = 5.5cm 
Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C. 
Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C. 
Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D. 
Step 6- Now join BC, CD and AD 
Measure of BD is 5.1cm. 
 
 
3. Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 
cm, WX = 3 cm and XZ = 9 cm. 
Solution: 
The given details are XY = 5cm, YZ = 6cm, ZW = 7cm, WX = 3cm and XZ = 9cm. 
Steps to construct a quadrilateral: 
Step 1- Draw line XZ of length 9cm. 
Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z 
as centre and radius ZY = 6cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. 
Similarly, taking Z as the center and radius ZW = 7cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
4. Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm, and QS = 
8.2 cm. 
Solution: 
The given details are PQ = 5.2 cm, PR = 6.8 cm, and QS = 8.2 cm. 
Steps to construct a parallelogram: 
Step 1- Draw line QS of length 8.2 cm. 
Step 2- Divide the line segment QS into half i.e 4.1 cm and mark that point as O. Now by 
taking O as center cut an arc on both the sides of O with a radius of 3.4cm each. And 
mark that points as P and R. 
Step 3- cut an arc by taking Q as a center and radius QR = 5.2cm to intersect with point 
R. 
Step 4- cut an arc by taking Q as a center and radius QP = 5.2cm to intersect with point P. 
Step 5- Join sides PQ, PS, QR and RS. 
 
 
5. Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other 
diagonal. 
Solution: 
The given details are side 6 cm and one diagonal 8 cm. 
We know all the sides of a rhombus are equal and diagonals bisect each other. 
Steps to construct a rhombus: 
Step 1- Draw a line XZ of length 8 cm. 
Step 2- By taking a radius of 6 cm, cut an arc by taking X as the center. Do the same by 
taking Z as centre with radius of 6 cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- Now for vertex W, by taking radius of 6 cm and cut an arc by taking X as the 
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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.1                                                  PAGE NO: 18.4 
 
1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 
cm, DA = 3.8 cm and BD = 6.6 cm. 
Solution: 
The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 
cm. 
Divide the quadrilateral into two triangles i.e., ?ABD and ?BCD 
Steps to construct a quadrilateral: 
Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm. 
Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as 
centre and radius CD = 6.4 cm. 
Step 3- Now join the intersection point from B and D and label it as C. 
Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. 
Do the same by taking D as center and radius DA = 3.8cm. 
Step 5- Join the intersection point from B and D and label it as A. 
 
 
2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 
6.3 cm, AC = 9.4 cm Measure BD. 
Solution: 
The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm 
Measure BD. 
Steps to construct a quadrilateral: 
Step 1- Draw a line segment AB = 5.5cm 
Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C. 
Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C. 
Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D. 
Step 6- Now join BC, CD and AD 
Measure of BD is 5.1cm. 
 
 
3. Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 
cm, WX = 3 cm and XZ = 9 cm. 
Solution: 
The given details are XY = 5cm, YZ = 6cm, ZW = 7cm, WX = 3cm and XZ = 9cm. 
Steps to construct a quadrilateral: 
Step 1- Draw line XZ of length 9cm. 
Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z 
as centre and radius ZY = 6cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. 
Similarly, taking Z as the center and radius ZW = 7cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
4. Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm, and QS = 
8.2 cm. 
Solution: 
The given details are PQ = 5.2 cm, PR = 6.8 cm, and QS = 8.2 cm. 
Steps to construct a parallelogram: 
Step 1- Draw line QS of length 8.2 cm. 
Step 2- Divide the line segment QS into half i.e 4.1 cm and mark that point as O. Now by 
taking O as center cut an arc on both the sides of O with a radius of 3.4cm each. And 
mark that points as P and R. 
Step 3- cut an arc by taking Q as a center and radius QR = 5.2cm to intersect with point 
R. 
Step 4- cut an arc by taking Q as a center and radius QP = 5.2cm to intersect with point P. 
Step 5- Join sides PQ, PS, QR and RS. 
 
 
5. Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other 
diagonal. 
Solution: 
The given details are side 6 cm and one diagonal 8 cm. 
We know all the sides of a rhombus are equal and diagonals bisect each other. 
Steps to construct a rhombus: 
Step 1- Draw a line XZ of length 8 cm. 
Step 2- By taking a radius of 6 cm, cut an arc by taking X as the center. Do the same by 
taking Z as centre with radius of 6 cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- Now for vertex W, by taking radius of 6 cm and cut an arc by taking X as the 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
center. Do the same by taking Z as center and radius of 6 cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
Step 6- Now join XY, XW, XZ and ZY 
 
 
6. Construct a kite ABCD in which AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm. 
Solution: 
The given details are AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm. 
Steps to construct a kite: 
Step 1- Draw line AC of length 7.2 cm. 
Step 2- By taking a radius of 4 cm and cut an arc by taking A as the center. Do the same 
by taking C as centre with radius of 4.9 cm. 
Step 3- Now join the intersection point from A and C and label it as B. 
Step 4- Now for vertex D, cut an arc by taking A as the center. Do the same by taking C 
as center with radius of 4.9 cm. 
Step 5- Join the intersection point from A and C and label it as D. 
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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.1                                                  PAGE NO: 18.4 
 
1. Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 
cm, DA = 3.8 cm and BD = 6.6 cm. 
Solution: 
The given details are AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA = 3.8 cm and BD = 6.6 
cm. 
Divide the quadrilateral into two triangles i.e., ?ABD and ?BCD 
Steps to construct a quadrilateral: 
Step 1- By using SSS congruency rule, Draw line BD of length 6.6 cm. 
Step 2- Cut an arc with B as the centre and radius BC = 4cm. Do the same by taking D as 
centre and radius CD = 6.4 cm. 
Step 3- Now join the intersection point from B and D and label it as C. 
Step 4- Now for vertex A, cut an arc by taking B as the center and radius BA = 4.4cm. 
Do the same by taking D as center and radius DA = 3.8cm. 
Step 5- Join the intersection point from B and D and label it as A. 
 
 
2. Construct a quadrilateral ABCD in which AB = BC = 5.5 cm, CD = 4 cm, DA = 
6.3 cm, AC = 9.4 cm Measure BD. 
Solution: 
The given details are AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3 cm, AC = 9.4 cm 
Measure BD. 
Steps to construct a quadrilateral: 
Step 1- Draw a line segment AB = 5.5cm 
Step 2- With B as center and radius BC = 5.5cm cut an arc. Mark that point as C. 
Step 3- With A as center and radius AC = 9.4cm cut an arc to intersect at point C. 
Step 4- With C as center and radius CD = 4cm cut an arc. Mark that point as D. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 5- With A as center and radius AD = 6.3cm cut an arc to intersect at point D. 
Step 6- Now join BC, CD and AD 
Measure of BD is 5.1cm. 
 
 
3. Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 
cm, WX = 3 cm and XZ = 9 cm. 
Solution: 
The given details are XY = 5cm, YZ = 6cm, ZW = 7cm, WX = 3cm and XZ = 9cm. 
Steps to construct a quadrilateral: 
Step 1- Draw line XZ of length 9cm. 
Step 2- Cut an arc by taking X as the centre radius XY = 5cm. Do the same by taking Z 
as centre and radius ZY = 6cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- For vertex W, cut an arc by taking X as the center and radius XW = 3cm. 
Similarly, taking Z as the center and radius ZW = 7cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
4. Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm, and QS = 
8.2 cm. 
Solution: 
The given details are PQ = 5.2 cm, PR = 6.8 cm, and QS = 8.2 cm. 
Steps to construct a parallelogram: 
Step 1- Draw line QS of length 8.2 cm. 
Step 2- Divide the line segment QS into half i.e 4.1 cm and mark that point as O. Now by 
taking O as center cut an arc on both the sides of O with a radius of 3.4cm each. And 
mark that points as P and R. 
Step 3- cut an arc by taking Q as a center and radius QR = 5.2cm to intersect with point 
R. 
Step 4- cut an arc by taking Q as a center and radius QP = 5.2cm to intersect with point P. 
Step 5- Join sides PQ, PS, QR and RS. 
 
 
5. Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other 
diagonal. 
Solution: 
The given details are side 6 cm and one diagonal 8 cm. 
We know all the sides of a rhombus are equal and diagonals bisect each other. 
Steps to construct a rhombus: 
Step 1- Draw a line XZ of length 8 cm. 
Step 2- By taking a radius of 6 cm, cut an arc by taking X as the center. Do the same by 
taking Z as centre with radius of 6 cm. 
Step 3- Now join the intersection point from X and Z and label it as Y. 
Step 4- Now for vertex W, by taking radius of 6 cm and cut an arc by taking X as the 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
center. Do the same by taking Z as center and radius of 6 cm. 
Step 5- Join the intersection point from X and Z and label it as W. 
Step 6- Now join XY, XW, XZ and ZY 
 
 
6. Construct a kite ABCD in which AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm. 
Solution: 
The given details are AB = 4 cm, BC = 4.9 cm, AC = 7.2 cm. 
Steps to construct a kite: 
Step 1- Draw line AC of length 7.2 cm. 
Step 2- By taking a radius of 4 cm and cut an arc by taking A as the center. Do the same 
by taking C as centre with radius of 4.9 cm. 
Step 3- Now join the intersection point from A and C and label it as B. 
Step 4- Now for vertex D, cut an arc by taking A as the center. Do the same by taking C 
as center with radius of 4.9 cm. 
Step 5- Join the intersection point from A and C and label it as D. 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
7. Construct, if possible, a quadrilateral ABCD given AB = 6 cm, BC = 3.7 cm, CD =
5.7 cm, AD = 5.5 cm and BD = 6.1 cm. Give reasons for not being able to construct
it, if you cannot.
Solution:
The given details are AB = 6 cm, BC = 3.7 cm, CD = 5.7 cm, AD = 5.5 cm and BD = 6.1
cm.
Steps to construct a quadrilateral:
Step 1- Draw a line AB of length 6cm.
Step 2- With A as a center cut an arc of radius 5.5cm and mark that point as D.
Step 3- With B as a center cut an arc of radius 6.1cm to intersect with point D.
Step 4- With B as a center cut an arc of radius 3.7cm and mark that point as C.
Step 5- With D as a center cut an arc of radius 5.7cm to intersect with point C.
Step 6- Now join AD, BD, BC and DC